Update 29th May 1997: generators for the Monster in its
196882-dimensional representation over GF(2) now exist
on computer. They are in a special format, requiring special
programmes to use them, so they are not being made
generally available at this time.

Update 19th November 1997: standard generators can now
be made as 196882 × 196882 matrices over GF(2), for the cost
of a few days of CPU time, but we do not have enough room to
write down the answer.

Update 15th December 1998: standard generators have now been made
as 196882 × 196882 matrices over GF(2) — this took about 8 hours CPU time
on a pentium machine. They have been multiplied together, using most
of the computing resources of Lehrstuhl D für Mathematik, RWTH Aachen,
for about 45 hours — completed 05:40 on December 14th.

Update January 2000: generators for the Monster in its
196882-dimensional representation over GF(3) now exist
on computer, constructed by Beth Holmes. They are in a special format, requiring special
programmes to use them, so they are not being made
generally available at this time.

Update October 2000: generators for the Monster in its
196883-dimensional representation over GF(7) now exist
on computer. They are in a special format, requiring special
programmes to use them, so they are not being made
generally available at this time.

Here we shall include some representations of some maximal subgroups
of the Monster, to facilitate calculations in these subgroups.
There are 43 classes of maximal subgroups known so far.
Any possible maximal subgroup which is not listed here has socle
isomorphic to one of the following simple groups:
L2(13), L2(27), Sz(8),
U3(4), U3(8).

31+12.2Suz.2, order
2 859 230 155 080 499 200. This group is a quotient
of the split extension 31+12:6Suz.2
by a normal subgroup of order 3. We give three generators
for this split extension, and the fourth element is
a generator for the subgroup of order 3 which has
to be factored out. It is now available as a faithful representation of dimension 78; no subgroup of order 3 needs to be factored out. NB: Word for A in Magma files corrected [up to inversion] on 24/8/04.
Available as

The group below is also of shape 53+3.(2 × L3(5)),
but is not isomorphic to a subgroup of the Monster.
[This group is not of shape 53+3:(2 × L3(5)) or (53 × 53).(2 × L3(5)) either.]
This group has been placed here for purposes of comparison.